► There are many theories of lexical access, which provide extensive accounts of lexical representations in the production process,( Levelt,1982,1999. Dell. 1986 ). In the present…
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▼ There are many theories of lexical access, which provide extensive accounts of lexical representations in the production process,( Levelt,1982,1999. Dell. 1986 ). In the present study we attempt to determine the relationship between the syntactic and phonological components of these representations. Primarily looking at whether this relationship is the same in children and adults. The study used 16 adult and 16 child participants. The children were aged between 3 and 4. We used the paradigm of syntactic priming, in an attempt to determine whether or not participants were more likely to produce a Noun Relative Clause utterance, just after they had comprehended the same structure. Also looking at whether or not children were more susceptible to this than adults. We also tested for a ‘learning effect’.
The task used for priming was a game of ‘snap’ adapted from Branigan, Mclean and Jones, (2005). In the ‘game’ pictures were described one by one in turn. Firstly by the experimenter: ‘the prime’ and then by the participant: ‘the target’. Each Prime and Target pair counted as one item of the experiment.
There was a main effect of prime for both the adult and child participants; this was significantly larger in the child participants. There was also a significant effect of ‘learning’ for the child participants but not the adults. There was a significant main effect of phonological relatedness in the adult group but not the child. There was also an interaction between prime and Phonological relatedness in the adult participants, where participants were more likely to be primed if the noun ‘heads’ were phonologically related. The results seem to indicate that phonological feedback is apparent in adults but not children, suggesting that the processes and representations involved in language production are not identical for adults and children.
Advisors/Committee Members: Branigan, Holly.

Ferguson, J. (2008). An Investigation into the Phonological and Syntactic Representations Involved in Language Production of Adults and Children: A Study Using the Paradigm of Syntactic Priming. (Thesis). University of Edinburgh. Retrieved from http://hdl.handle.net/1842/2892

Note: this citation may be lacking information needed for this citation format:Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Ferguson, Janet. “An Investigation into the Phonological and Syntactic Representations Involved in Language Production of Adults and Children: A Study Using the Paradigm of Syntactic Priming.” 2008. Thesis, University of Edinburgh. Accessed February 22, 2019.
http://hdl.handle.net/1842/2892.

Note: this citation may be lacking information needed for this citation format:Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Ferguson, Janet. “An Investigation into the Phonological and Syntactic Representations Involved in Language Production of Adults and Children: A Study Using the Paradigm of Syntactic Priming.” 2008. Web. 22 Feb 2019.

Vancouver:

Ferguson J. An Investigation into the Phonological and Syntactic Representations Involved in Language Production of Adults and Children: A Study Using the Paradigm of Syntactic Priming. [Internet] [Thesis]. University of Edinburgh; 2008. [cited 2019 Feb 22].
Available from: http://hdl.handle.net/1842/2892.

Note: this citation may be lacking information needed for this citation format:Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Ferguson J. An Investigation into the Phonological and Syntactic Representations Involved in Language Production of Adults and Children: A Study Using the Paradigm of Syntactic Priming. [Thesis]. University of Edinburgh; 2008. Available from: http://hdl.handle.net/1842/2892

Note: this citation may be lacking information needed for this citation format:Not specified: Masters Thesis or Doctoral Dissertation

► In this master thesis I have looked on two different kinds of representations of the Lie algebras su(2) and sl(2), and the tensor products…
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▼ In this master thesis I have looked on two different kinds of representations of the Lie algebras su(2) and sl(2), and the tensor products of the representations. In the first case I looked at a tensor product involving a representation similar to one that appears in an article by A. van Tonder. This representation and tensor product was investigated mainly to get a good comprehension in the subject and to understand some of the problems that can arise. In the other case, which is the main problem in this thesis, I looked at a tensor product and representations that appears in an article by M. R. Gaberdiel. Here we deal with a tensor product of representations of su(2) with a specific value for the level at k = -4/3 and a specific eigenvalue of the Casimir operator at -2/9. This was done in the frame of finite dimensional Lie algebra and affine Lie algebra and not in the case of fusion rules as in the article by M. R. Gaberdiel. In both cases some of the calculations where done from in situ and the investigation of the representations behaviour due to the step operators, theirs eigenvalue and theirs weight system. Results and conclusions of the investigations are discussed in the last part of this thesis.

► Using both quantitative and qualitative data collection and analyses techniques, this study examined representations used by sixteen (n = 16) teachers while teaching the concepts…
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▼ Using both quantitative and qualitative data collection and analyses techniques, this study examined representations used by sixteen (n = 16) teachers while teaching the concepts of converting among fractions, decimals, and percents. The classroom videos used for this study were recorded as part of the Middle School Mathematics Project (MSMP). The study also compared teacher-selected and textbook representations and examined how teachers? use of idiosyncratic representations influenced representational choices on the number test by the teachers? five hundred eighty-one (N = 581) students.
In addition to using geometric figures and manipulatives, a majority of the teachers used natural language such as the words nanny, north, neighbor, dog, cowboy, and house to characterize fractions and mathematical procedures or algorithms. Coding of teacher-selected representations showed that verbal representations deviated from textbook representations the most. Some teachers used the words or phrases bigger, smaller, doubling, tripling, breaking-down, and building-up in the context of equivalent fractions. There was widespread use of idiosyncratic representations by teachers, such as equations with missing or double equal signs, numbers and operators written as superscripts, and numbers written above and below the equal sign. Although use of idiosyncratic representations by teachers influenced representational choices by students on the number test, no evidence of a relationship between representational forms and degree of correctness of solutions was found. The study did reveal though that teachers? use of idiosyncratic representations can lead to student misconceptions such as thinking that multiplying by a whole number not equal to 1 gives an equivalent fraction. Statistical tests were done to determine if frequency of representation usage by teachers was related to the textbook, highest degree obtained by teacher, certification, number of years spent teaching mathematics, number of years teaching mathematics at grade level, number of hours completed on professional development related to their textbook, and total number of days spent on the Interagency Education Research Initiative (IERI) professional development. The results showed representation usage was related to all the above variables, except the highest degree obtained and the total number of days spent on the IERI professional development.
Advisors/Committee Members: Capraro, Robert M (advisor), Capraro, Mary M (committee member), Kulm, Gerald (committee member), Rojas, Maurice J (committee member), Viruru, Radhika (committee member).

► As mentioned in [8], A group representation can be thought of as an action oi a group G on some vector space. Such actions arise…
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▼ As mentioned in [8], A group representation can be thought of as an action
oi a group G on some vector space. Such actions arise naturally in many
branches oi mathematics and physics and as such it is important to study
and understand the theory of representations. Cayley's theorem asserts that
everv finite group can be embedded in a group of symmetries Sn for some n
- this makes the studies related to the symmetric group of much significance
since by the isomorphism guaranteed by the Cayley’s theorem we may un
derstand the properties of any other finite group.
A* an illustration, the solution space of a differential equation in a 3-dimensional
?pace having a rotational symmetry has its solution space invariant under ro
tations. Thus the space of solutions will constitute a representation of the
rotation group 50(3). If we know what all of the representations of 50(3)
are, then this can help immensely in narrowing down what the space of so
lutions can be.
In fact, one of the chief applications of representation theory is to exploit
symmetry. If a system has symmetry, then the set of symmetries will form a
group, and understanding the representations of the symmetry group allows
us to use that symmetry to simplify the problem
This report focuses on the representation theory of symmetric groups and
in particular on the construction of -ill irreducible modules of the symmet-
lic group 5;i 'Otherwise known as the Specht Modules). There are numerous
applications of representation of groups and in particular tiie representa
tion of the symmetric group. For instance, they arise in physics, probability
v
and statistics, topological graph theory, the theory of partially ordered sets
amongst many other areas.
This report contains 5 chapters - in chapter 1 we have provided elementary
definitions as well as basic results about the symmetric group Sn. Chapter 2
is on the ordinary representation of finite group with some small emphasis on
the symmetric group Sn. It should be noted that this chapter is not exhaus
tive as far as representation theory is concerned, we have only mentioned
some useful aspects that is in direct reference to the main objective of this
report. In chapter 3 we have dwelt on the construction of the ordinary irre
ducible modules of the symmetric group Sn popularly known as the Specht
modules, and a simple example for the case n = 3 has been given.
In representation theory of finite groups, it is useful to know which ordi
nary irreducible representations remain irreducible when reduced modulo a
prime p. In chapter 4. we have traced the history of classification of ordinary
irreducible modules that remain irreducible modulo p.

► Because of all the media attention the democratic candidates get, their media representation is of the utmost importance. So, how are Barack Obama and Hillary…
(more)

▼ Because of all the media attention the democratic candidates get, their media representation is of the utmost importance. So, how are Barack Obama and Hillary Rodham Clinton represented in their media campaigns? And what role do racial and gender stereotypes play in these representations? In order to answer these questions, I will research the websites of the candidates which give an up to date overview of the images, speeches, texts, issues and videos as used in the media campaigns of the candidates. In the conclusion I will also position the candidates in the debate concerning empowerment and post-ethnicity in terms of representation.
Advisors/Committee Members: Boter, B..

► Dressage is an elitist equestrian sport that is a remnant of imperial culture. It has been a sport and an art for centuries. It is…
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▼ Dressage is an elitist equestrian sport that is a remnant of imperial culture. It has been a sport and an art for centuries. It is in the 21st century that dressage is finding it hard to reinvent itself. This communications thesis deals with the different representations of dressage throughout history. It focuses on the intended messages produced and the multiple layers of received messages, which may or may not match what was intended and why. It also examines the motivation behind these messages and how they have become naturalized and reside in the realm of myth. The paper uses the key concepts of simulacra, myth, taste, colonialism, and reinvention to explain the process of making meaning. They reveal structures of power and dominance, social class formation, stereotypes, cultural knowledge, the changes in representation, and the taken for granted. Ethnography and critical discourse analysis are the two methods employed to examine the representations. A detailed history of dressage is provided to show the palimpsest of representations and the layers of reinvented representations that cover it based on historical context. It looks at the pageants of nobility, the circus, competitive dressage, and classical dressage as well as a few modern representations. Each of the representations is a display or performance. They each tell a story. By understanding each representation as a story, one is able to extrapolate the meaning. No matter what representation is selected, the same process of encoding and decoding exists. The elite who perform dressage convey an intentional message with specific motivation to the receiver who may read many layers of meaning in the text other than what was intended. The history of dressage allows us to examine how these interpretations came to pass. This paper provides a model for understanding how other high culture can grow an audience and remain relevant to the modern age.
Advisors/Committee Members: Nakho Kim, Thesis Advisor.

► This research is based on Middle School Mathematics Project (MSMP) funded by the Interagency Educational Research Initiative through a grant to the American Association for…
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▼ This research is based on Middle School Mathematics Project (MSMP) funded
by the Interagency Educational Research Initiative through a grant to the American
Association for the Advancement of Science. Both teacher??????s instructional
representations and students?????? written representations were coded and analyzed to
investigate the nature and structure of the representations in teaching fractions, decimals
and percents in middle school classrooms in three school districts in Texas. The study
further explored the relationship between both the quality and quantity of instructional
representations and students?????? written representations, and the relationship between
students?????? written representations and their achievements.
This dissertation used a mixed approach utilizing both quantitative and
qualitative methods. The data was collected in the first two years of a five-year study. A
total of 14 sixth grade mathematics teachers from three school districts in Texas were
selected from the MSMP project. Before the actual videotaping procedure, a professional
development focusing on multiple representations was held for the teachers. Both pretests and posttests were used to examine the relationship between the structure of
students?????? written representations and their achievements.
The results showed that the both the quantity and quality of teachers??????
instructional representations varied a lot. Symbolic representations were the predominant
representations in classroom teaching. Structures of instructional representations
converge to content sub-constructs rather than format sub-constructs. Here subconstructs
include part-whole, measure, quotient, multiplication by one and cross
product. Instead, format sub-constructs include real world, manipulatives, pictures,
spoken symbolic representations and written symbolic representations, however,
connections between these sub-constructs were not statistically significant. Within the
three content sub-constructs (part-whole, quotient, and multiplication by one) that
revealed by students?????? written representations, quotient and multiplication by one
significantly predicated the students?????? posttest scores. It was also found that, among the
three quality criteria (accuracy, comprehensibility and connections) of instructional
representations, the comprehensibility score significantly predicated students??????
achievement in the posttests.
Advisors/Committee Members: Kulm, Gerald (advisor), Lamb, Charles (committee member), Loving, Cathleen (committee member), Willson, Victor (committee member).

In this research we set out to study and compare the content of representations of
non-disabled students in the face of disabilities, particularly in the face of Down syndrome.
In a sample of 50 students, aged between 12 and 14 years, there were two groups
concerning the variable contact - direct contact group, and null contact group - and two
groups concerning the variable skills of parents - in that group both parents had a basic
education, and group where one of the parents had secondary or higher education.
The research instrument used was the interview, and the data were explored by
analyzing the content and then, by statistical analysis, using the Mann-Whitney and Chi-
Square tests.
We can conclude that some of the representations of students vary according to
proximity (contact), and that in general the students showed positive representations against
the integration of children with Down syndrome in regular schools.
However, these offices do not vary significantly depending on the parenting skills.

First, from a theoretical perspective, this thesis makes reference to existing literature toexamine the notion of the professional teacher and the approaches that have been set up toencourage his/her development. Secondly, it seeks to contextualise this notion within theKenyan context and, specifically, analyse the evolution of the teaching profession based onhistorical data as well as on an empirical study carried out amongst student teachers. In thisregard, this thesis analyses the emergence and evolution of the teaching profession in Kenyawhile placing a particular emphasis on social and professional representations. Finally, thiswork examines the sense that educational policies and pre-service student teachers accord tothe notion of the “professional teacher”.

► This thesis explores the representations of Blackness constructed and embraced by Saadakeem Papa Kyriakos, the prophet and leader of the Church of Cristo Kyrios, a…
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▼ This thesis explores the representations of Blackness
constructed and embraced by Saadakeem Papa Kyriakos, the prophet
and leader of the Church of Cristo Kyrios, a marginal organization
located in Lima, Peru. Saadakeem proudly claims to adhere to the
religion practiced by plantation slaves in Peru in the sixteenth
century. This thesis presents and analyzes some of Saadakeem’s
divine messages about slavery as well as the images of Black men he
creates, adopts and employs to symbolize the sacred Black figures
the Church worships. This thesis contends that Saadakeem’s
representations of Blackness not only exclude women, but also
reinforce deeply entrenched racial conceptualizations that depict
Black men as mindless, primitive and sexual bodies.

Carroll, N. M. (2012). Remaking the Slave Past in the Present: Representations of
Afro-Peruvian Men in the Church of Cristo Kyrios. (Masters Thesis). University of Alberta. Retrieved from https://era.library.ualberta.ca/files/2v23vv60b

Chicago Manual of Style (16th Edition):

Carroll, Natacha Margarita. “Remaking the Slave Past in the Present: Representations of
Afro-Peruvian Men in the Church of Cristo Kyrios.” 2012. Masters Thesis, University of Alberta. Accessed February 22, 2019.
https://era.library.ualberta.ca/files/2v23vv60b.

MLA Handbook (7th Edition):

Carroll, Natacha Margarita. “Remaking the Slave Past in the Present: Representations of
Afro-Peruvian Men in the Church of Cristo Kyrios.” 2012. Web. 22 Feb 2019.

Vancouver:

Carroll NM. Remaking the Slave Past in the Present: Representations of
Afro-Peruvian Men in the Church of Cristo Kyrios. [Internet] [Masters thesis]. University of Alberta; 2012. [cited 2019 Feb 22].
Available from: https://era.library.ualberta.ca/files/2v23vv60b.

Council of Science Editors:

Carroll NM. Remaking the Slave Past in the Present: Representations of
Afro-Peruvian Men in the Church of Cristo Kyrios. [Masters Thesis]. University of Alberta; 2012. Available from: https://era.library.ualberta.ca/files/2v23vv60b

► We present a complete acyclic matching of the Hasse diagram associated with the face lattice of a hypersimplex. Since a hypersimplex is a convex…
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▼ We present a complete acyclic matching of the Hasse diagram associated with the face lattice of a hypersimplex. Since a hypersimplex is a convex polytope, there is a natural way to form a CW complex from its faces. We will then utilize this matching along with discrete Morse theory and some topological techniques to classify every subcomplex whose reduced homology groups are concentrated in a single degree. These reduced homology groups support a natural action of the symmetric group and a description of the characters that this action produces is given.
Advisors/Committee Members: Richard M. Green, Nathaniel Thiem, Marty Walter.

Sen, I. (1995). Representations of women in the fiction of the British
raj in the 19th Century; -. (Thesis). Jawaharlal Nehru University. Retrieved from http://shodhganga.inflibnet.ac.in/handle/10603/30118

Note: this citation may be lacking information needed for this citation format:Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Sen, Indrani. “Representations of women in the fiction of the British
raj in the 19th Century; -.” 1995. Thesis, Jawaharlal Nehru University. Accessed February 22, 2019.
http://shodhganga.inflibnet.ac.in/handle/10603/30118.

Note: this citation may be lacking information needed for this citation format:Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Sen, Indrani. “Representations of women in the fiction of the British
raj in the 19th Century; -.” 1995. Web. 22 Feb 2019.

Vancouver:

Sen I. Representations of women in the fiction of the British
raj in the 19th Century; -. [Internet] [Thesis]. Jawaharlal Nehru University; 1995. [cited 2019 Feb 22].
Available from: http://shodhganga.inflibnet.ac.in/handle/10603/30118.

Note: this citation may be lacking information needed for this citation format:Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Sen I. Representations of women in the fiction of the British
raj in the 19th Century; -. [Thesis]. Jawaharlal Nehru University; 1995. Available from: http://shodhganga.inflibnet.ac.in/handle/10603/30118

Note: this citation may be lacking information needed for this citation format:Not specified: Masters Thesis or Doctoral Dissertation

University of Edinburgh

13.
Balfour, Camilla.
Does the social context change how we interact with one another in joint activity?.

► The interdependency of action and perception has illustrated how shared representations between co-actors facilitate successful joint activity. Recent studies in action based experiments have explored…
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▼ The interdependency of action and perception has illustrated how shared representations between co-actors facilitate successful joint activity. Recent studies in action based experiments have explored the extent to which shared representations are formed in cooperative and competitive social contexts. We explore whether these social contexts also have a different effect on shared representations in a more integrated form of joint action, that of dialogue. Participants were recruited in same sex groups of 4 and were randomly assigned to 2 teams of 2: Team A and Team B. They consecutively carried out a shared Stroop task in two differing social conditions, once cooperatively and once competitively. For the cooperative condition, each team of 2 were required to work together to collaboratively beat the response times of the other team. For the competitive condition, a member from each opposing team carried out the shared Stroop task together in competition to try and beat each other’s response times. The order of these conditions was alternated between different groups of 4. In this way the results revealed that between the social contexts there was a significant difference of congruency effect, but only when the cooperative context preceded the competitive context and not when the conditions were carried out in the opposite sequence. Furthermore, participants responded slower to stimuli in the first part of the experiment compared to the second part, irrelevant of contextual manipulation. Limitations of the study are discussed in explanation of these results. Implications suggest that when the social context elicits conflicting goals with alignment, shared representations occur to a lesser extent, even in this more integrated form of joint action, dialogue. To understand the underlying mechanisms in joint action, future research needs to take into account the social context in which joint action is embedded.
Advisors/Committee Members: Pickering, Martin J..

Balfour, C. (2011). Does the social context change how we interact with one another in joint activity?. (Thesis). University of Edinburgh. Retrieved from http://hdl.handle.net/1842/6172

Note: this citation may be lacking information needed for this citation format:Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Balfour, Camilla. “Does the social context change how we interact with one another in joint activity?.” 2011. Thesis, University of Edinburgh. Accessed February 22, 2019.
http://hdl.handle.net/1842/6172.

Note: this citation may be lacking information needed for this citation format:Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Balfour, Camilla. “Does the social context change how we interact with one another in joint activity?.” 2011. Web. 22 Feb 2019.

Vancouver:

Balfour C. Does the social context change how we interact with one another in joint activity?. [Internet] [Thesis]. University of Edinburgh; 2011. [cited 2019 Feb 22].
Available from: http://hdl.handle.net/1842/6172.

Note: this citation may be lacking information needed for this citation format:Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Balfour C. Does the social context change how we interact with one another in joint activity?. [Thesis]. University of Edinburgh; 2011. Available from: http://hdl.handle.net/1842/6172

Note: this citation may be lacking information needed for this citation format:Not specified: Masters Thesis or Doctoral Dissertation

► In this study Finnish history teacher's conceptions and experiences on national history teaching are explored. As representatives of educational institution, teachers are situated in intersection…
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▼ In this study Finnish history teacher's conceptions and experiences on national history teaching are explored. As representatives of educational institution, teachers are situated in intersection point of official history curriculum, academic research, family histories and common sense understandings of history. Another point of this study is to find out what kind of mainstream narrative of national history is mediated at schools which are its focal elements and what is possibly excluded. Which possibly sensitive or controversial elements are present in history teaching are also studied.
Theoretical background of this study can be divided in two parts. First part consists of social psychological approaches to studying history-related issues, especially Serge Moscovici's Social Representations Theory. The theory explores how common sense knowledge is constructed in social interaction. The second part consists of previous studies on history science and history didactics. Turning points in Finnish history and previous studies on national collective memory are introduced. Also different approaches to history teaching and how Finnish school history is in relation to them is discussed.
The empirical part of this study consists of Finnish history teachers' individual interviews (N=11). Participants are teachers both at high school and upper comprehensive level schools mostly situated in Helsinki capital region. They have varying experience in teaching history and other subjects. The interview scheme consists of both open questions and statements. All interviews were conducted in Finnish, recorded and transcribed. The analysis of the interview data is based on Charmaz' (2006) version of Grounded theory.
Main results of the study show that teachers' representations of history teaching are mostly 'enlightened' and 'skill-oriented' which are in line with official curriculum. More 'traditional' or 'romantic' representations of school history were present, although marginal in this sample. The values and aims that guide teachers' work are manifested in seven different roles that were found in this study: 'initiator of interest in history', 'creator of historical understanding', 'developer of critical thinking', 'mediator of scientific knowledge, facts and truth', 'mediator of values and attitudes', 'civic educator' and 'independent actor'. History is seen as educational and challenging subject which ought to develop student's ability to critical thinking, multiperspectivity, tolerance and overall understanding of the world.
Main history narrative found in this study consists of eight hegemonic representations. This narrative is named as 'Coming-of-age-story' or 'Cinderella story' The cores of history representations form a combination of elements on which national history curriculum could be based: birth, development, unity, heroism, victimhood, balancing and belonging. These are powerful narrative elements through which national identity could be constructed in school history. Alternative/ marginal narratives also take part…

► Developmental dyslexia is widely believed to be caused either mainly or in part by an impairment of phonological representations. Although this hypothesis predicts that individuals…
(more)

▼ Developmental dyslexia is widely believed to be caused either mainly or in part by an impairment of phonological representations. Although this hypothesis predicts that individuals with dyslexia should show deficits in tasks which require the use of implicit phonological knowledge, this has not yet been directly tested, as the evidence cited in support of this hypothesis usually comes from metalinguistic tasks which demand explicit awareness of phonological units. Additionally, since the ability to perform metalinguistic tasks which involve phonological segments can be enhanced by an individual’s competence in alphabetic literacy, the possibility remains that phonological skills may have been inadequately isolated from the influences of literacy acquisition in many cases. The study reported in this thesis investigated both the representations and the metalinguistic skills of a group of adults with a history of developmental dyslexia, examining areas of phonology which do and do not have orthographic counterparts. To isolate phonological skills from orthographic skills, the representations of conventional segmental contrasts (e.g. /k/ vs /g/) were compared with the representation of suprasegmental contrasts (as seen in minimal pairs such as ′toy factory and toy ′factory), which have no orthographic counterpart. Basic metalinguistic skills were tested by means of a phonological awareness task targeting both segmental and suprasegmental units, and phonological manipulation skills were tested using a Pig Latin task and a Spoonerism task, where participants were required to manipulate both segmental and suprasegmental units (e.g. extracting the segment /b/ from consonant clusters and the main stress from SWW or WSW stress patterns). The results showed that although the performance of the dyslexic group was weaker than that of the control group when tasks required the manipulation of either the segmental or suprasegmental components of words, no evidence was found for a deficit in the tasks which drew on implicit representations or basic metalinguistic skills. These findings suggest that the phonological deficit in dyslexia may be restricted to the ability to manipulate phonological units rather than in the representation of them per se.

Dickie CE. Exploring the nature of the phonological deficit in dyslexia : are phonological representations impaired?. [Doctoral Dissertation]. University of Edinburgh; 2009. Available from: http://hdl.handle.net/1842/5944

The Ohio State University

16.
Nikolov, Martin Bozhidarov.
Construction of Series of Degenerate Representations for
GSp(2) and PGL(n).

► The relative trace formula is a tool for studying automorphic representations on symmetric spaces. In this work two relative trace formulas are studied: One…
(more)

▼ The relative trace formula is a tool for
studying automorphic representations on symmetric spaces. In this
work two relative trace formulas are studied: One for GSp(2)
relative to a form of SO(4) and one for PGL(n) relative to GL(n-1).
The first trace formula is used to study the
Saito-Kurokawa lifting of automorphic representations from PGL(2)
to PGSp(2), thus characterizing the image as the representations
with a nonzero period for the special orthogonal group SO(4,E/F)
associated to a quadratic extension E of the base field F, and a
nonzero Fourier coefficient for a generic character of the
unipotent radical of the Siegel parabolic subgroup.
The second trace formula is used to study the
representations pi of PGL(n), which have a nonzero linear form
invariant under the Levi subgroup GL(n-1), and a certain
nonvanishing degenerate Fourier coefficient, over local and global
fields. The result is that these pi are of the form I(1n-2,pi'),
namely normalizedly induced from the parabolic subgroup of type
(n-2, 2), trivial representation on the GL(n-2)-factor and cuspidal
pi' on the PGL(2)-factor. The analysis of the formula is intricate
our main achievement is rigorously establishing the convergence of
the formula. New in this case is that none of the representations
of PGL(n) involved are cuspidal, they rather occur in the
continuousspectrum, but discretely in our
formula.
Advisors/Committee Members: Flicker, Yuval (Advisor).

Nikolov, M. B. (2008). Construction of Series of Degenerate Representations for
GSp(2) and PGL(n). (Doctoral Dissertation). The Ohio State University. Retrieved from http://rave.ohiolink.edu/etdc/view?acc_num=osu1211149487

Chicago Manual of Style (16th Edition):

Nikolov, Martin Bozhidarov. “Construction of Series of Degenerate Representations for
GSp(2) and PGL(n).” 2008. Doctoral Dissertation, The Ohio State University. Accessed February 22, 2019.
http://rave.ohiolink.edu/etdc/view?acc_num=osu1211149487.

Nikolov MB. Construction of Series of Degenerate Representations for
GSp(2) and PGL(n). [Doctoral Dissertation]. The Ohio State University; 2008. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=osu1211149487

► Saeed [11] has considered Schur multipliers of some of the finite abelian groups.The study of the schur multipliers of abelian groups is the first step…
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▼ Saeed [11] has considered Schur multipliers of some of the finite abelian groups.The study of the schur multipliers of abelian groups is the first step in the studying of the projective representations of such groups. Our objective here is to determine the Inequivalent Irreducible projective representations of these groups which correspond to certain classes of factor sets.
Let On'denote the direct product of n cyclic m groups C of order m.Then in [9] and [10] the
a-regular classes have been determined; these being the classes at which non trivial projective representations with factor set a take on non zero character values. Here we review these results, and determine the Inequivalent Irreducible characters corresponding to these oc-regular classes. In particular, a complete set of irreducible inequivalent projective characters is obtained for these classes.The following is a brief description of how the work in the sequel has been organised. Chapter one gives the basic facts about factor sets and projective representations of finite groups together with some of their properties. The concepts of schur multipliers and twisted group algebras are also considered. The central and stem extensions of finite groups are discussed in chapter two; while chapter three is concerned with projective character theory. Here the interest is in reviewing those properties of projective characters which are analogous to those of ordinary characters. Finally the work in the previous chapters is applied in chapter four to obtain the irreducible projective characters of certain finite abelian groups; and the results follow the works of Morris and Saeed (c.f [8], [9], [10] and [11].)

An analysis of the different Hollywood movies on the Vietnam War and the way in which they represent America's most controversial foreign conflict; starting with Samuel Fuller's China Gate (1957) and ending with Werner Herzog's Rescue Dawn (2006).
Advisors/Committee Members: Rossem, Maarten van.

19.
Hangula, Teopolina O.
Literary representations of stigmatisation and myths surrounding death in the novels The Purple Violent of Oshaantu by Neshani Andreas and The other Presence by Francis Sifiso Nyathi
.

► This research study is an analysis of literary representation of stigmas and myths associated with death in the two selected novels, namely: The Purple Violet…
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▼ This research study is an analysis of literary representation of stigmas and myths associated with death in the two selected novels, namely: The Purple Violet of Oshaantu by Neshani Andreas and The Other Presence by Francis Sifiso Nyathi. The two novels analysed in this research project were selected because they both emphasised on the theme of death. The thesis used The Social Dominance Theory to analyse the impacts that stigmas and myths associated with death usually have on the victims. The study revealed that widows are often mistreated by their husbands’ families and relatives as portrayed by Andreas in The Purple Violet of Oshaantu. Equally, the study revealed how mostly those who are closely related to the deceased are mistreated by the mourners and the community as portrayed by Nyathi in The Other Presence. Furthermore, the study showed that education can be used to help eradicate myths and stigmas associated with death. All in all these two books offer a voice to the voiceless people who have lost their loved ones such as Mee Kauna, Mee Saara and Elder Sinvula to stand up for themselves and not let myths and stigmas associated with death silence them.

Hangula, T. O. (2016). Literary representations of stigmatisation and myths surrounding death in the novels The Purple Violent of Oshaantu by Neshani Andreas and The other Presence by Francis Sifiso Nyathi
. (Thesis). University of Namibia. Retrieved from http://hdl.handle.net/11070/1929

Note: this citation may be lacking information needed for this citation format:Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Hangula, Teopolina O. “Literary representations of stigmatisation and myths surrounding death in the novels The Purple Violent of Oshaantu by Neshani Andreas and The other Presence by Francis Sifiso Nyathi
.” 2016. Thesis, University of Namibia. Accessed February 22, 2019.
http://hdl.handle.net/11070/1929.

Note: this citation may be lacking information needed for this citation format:Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Hangula, Teopolina O. “Literary representations of stigmatisation and myths surrounding death in the novels The Purple Violent of Oshaantu by Neshani Andreas and The other Presence by Francis Sifiso Nyathi
.” 2016. Web. 22 Feb 2019.

Vancouver:

Hangula TO. Literary representations of stigmatisation and myths surrounding death in the novels The Purple Violent of Oshaantu by Neshani Andreas and The other Presence by Francis Sifiso Nyathi
. [Internet] [Thesis]. University of Namibia; 2016. [cited 2019 Feb 22].
Available from: http://hdl.handle.net/11070/1929.

Note: this citation may be lacking information needed for this citation format:Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Hangula TO. Literary representations of stigmatisation and myths surrounding death in the novels The Purple Violent of Oshaantu by Neshani Andreas and The other Presence by Francis Sifiso Nyathi
. [Thesis]. University of Namibia; 2016. Available from: http://hdl.handle.net/11070/1929

Note: this citation may be lacking information needed for this citation format:Not specified: Masters Thesis or Doctoral Dissertation

▼ Let E be an elementary abelian p-group of rank r and k an algebraically closed field of characteristic p. We investigate finitely generated kE-modules of stable constant Jordan type [a][b] with 1 ≤ a, b ≤ p − 1 using the functors Fi from finitely generated kE-modules to vector bundles on the projective space Pr−1 constructed by Benson and Pevtsova. In particular, we study relations on the Chern numbers of the trivial bundle M to obtain restrictions on a and b for sufficiently large ranks and primes. We then study kE-modules with the constant image property and define the constant image layers of a module with respect to its maximal submodule having the constant image property. We prove that almost all such subquotients are semisimple. Focusing on the class of W-modules in rank two, we also calculate the vector bundles Fi(M) for all W-modules M. For E of rank two, we derive a duality formula for kE-modules M of constant Jordan type and their generic kernels K(M). We use this to answer a question of Carlson, Friedlander and Suslin regarding whether or not the submodules J−iK(M) also have constant Jordan type for all i ≥ 0. We show that this question has an affirmative answer whenever p = 3 or J2K(M) = 0. We also show that it has a negative answer in general by constructing a kE-module M of constant Jordan type for p ≥ 5 such that J−1K(M) does not have constant Jordan type. Finally, we use ideas from a theorem of Benson to show that if M is a kE-module of constant Jordan type containing no Jordan blocks of length one, then there always exist submodules of J−1K(M)/J2K(M) having a particularly nice structure.

► In this thesis I will describe the theta correspondence for the reductive dual pairs (Sp(p,q),O*(4)) in terms of Langlands parameters. For the general reductive dual…
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▼ In this thesis I will describe the theta correspondence for the reductive dual pairs (Sp(p,q),O*(4)) in terms of Langlands parameters. For the general reductive dual pairs (Sp(p,q),O*(2n)), the explicit theta correspondence has been given in [21] for the case p + q ≤ n. So in this thesis we only need to consider the case p + q > 2. The main techniques used in this thesis are the correspondence in joint harmonic space and induction principle. The induction principle was first observed by Rallis and further developed by Moeglin. Combined with the result of correspondence on infinitesimal characters by Przebinda, I could give the explicit Howe correspondence for reductive dual pairs (Sp(p,q),O*(4)) in terms of Langlands parameters for almost cases.

► In this thesis, we give a full and explicit description of the local theta correspondence for all the dual pairs (O(p,q), Sp(2n,R)) with p +…
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▼ In this thesis, we give a full and explicit description of the local theta correspondence for all the dual pairs (O(p,q), Sp(2n,R)) with p + q = 4 for all n, in terms of Vogan's version of Langlands parameters. As a by-product, we get an explicit version of Induction Principle to compute the local theta correspondence for (O(p,q), Sp(2n,R)) with p + q even: when p + q ≤ 2n, the parameters of a theta (n + 1)-lift of a representation of O(p,q) is got from the parameters of its theta n-lift, if the n-lift is non-zero; similarly, when p + q ≥ 2n + 2, the theta (p + 1, q + 1)-lift of a representation of Sp(2n,R) is got from its theta (p,q)-lift, if the (p,q)-lift is non-zero. When p + q = 4, by our Explicit Induction Principle, and some standard results about first occurrences of local theta correspondence, we indeed reduce the computation to theta 4-lifts of determinant characters and theta 3-lifts for other irreducible admissible representations of O(p,q). Our strategy is to determine the resulting representation by its infinitesimal character and lowest K-types.

▼ Three experiments investigated efficient belief tracking as described by the two-systems theory of human mindreading (Apperly & Butterfill, 2009) whereupon mindreading implies the operation of a flexible system that is slow to develop and cognitively effortful, and an efficient system which develops early but subject to signature limits. Signature limits have been evidenced by children’s and adults’ difficulty anticipating how someone with a false belief (FB) about an object’s identity, will act. In a recent investigation of signature limits, erroneous pre-activation of the motor system was detected when adults predicted the actions of an agent with an identity FB, suggesting that efficient mindreading and motor processes are linked (Edwards & Low, 2017). Moreover, young children differentiated between true and FBs about an object’s location, but not identity, as revealed by the object children retrieved in an active helping task (Fizke et al., 2017). The aim of the present thesis was to provide new evidence of signature limits in adults, and of the recent conjecture that efficient mindreading and motor processes interact. In helping tasks, participants’ interpretation of another’s actions is crucial to how they coordinate their helping response. Therefore, an ecologically valid helping task was adapted to investigate the proposed interface between efficient mindreading and motor processes. The present work measured adults’ eye movements made prior to helping, and their helping actions across a set of distinct directional full-body movements (around which side of a desk they swerved, which compartment they approached, toward which compartment they reached, and which object they retrieved). In this way, it was possible to investigate whether gaze direction correlated with full-body movements and whether adults’ gaze differed when the agent’s FB was about an object’s location or identity. Results from Experiment 1 indicated that efficient belief tracking is equipped to process location but not identity FBs, and that - in the location scenario - gaze direction correlated with the immediate stage of participants’ helping action (the direction they swerved). To investigate this correlation further, Experiment 2 drew upon research suggesting that temporarily tying an observer’s hands behind their backs impaired their ability to predict the outcome of hand actions (Ambrosini et al., 2012). Results showed that tying adults’ hands behind their back had a negative effect on their gaze behavior and severed the correlation between gaze and swerving, suggesting that the link between efficient mindreading and motor processes is fragile. Experiment 3 tested an alternative interpretation for Experiment 2’s findings (that restraining participants’ hands applied a domain-general distraction, rather than a specific detriment to belief tracking) by tying up participants’ feet. Results were ambiguous: the gaze behavior of participants whose feet were tied did not differ from those who were unrestrained, nor from those whose hands were…
Advisors/Committee Members: Low, Jason.

Maymon, C. (2018). Exploration of Relations between Belief-Tracking and Motor Processing using a new Ecologically-Valid Helping Task for Adults. (Doctoral Dissertation). Victoria University of Wellington. Retrieved from http://hdl.handle.net/10063/7800

Chicago Manual of Style (16th Edition):

Maymon, Christopher. “Exploration of Relations between Belief-Tracking and Motor Processing using a new Ecologically-Valid Helping Task for Adults.” 2018. Doctoral Dissertation, Victoria University of Wellington. Accessed February 22, 2019.
http://hdl.handle.net/10063/7800.

MLA Handbook (7th Edition):

Maymon, Christopher. “Exploration of Relations between Belief-Tracking and Motor Processing using a new Ecologically-Valid Helping Task for Adults.” 2018. Web. 22 Feb 2019.

Vancouver:

Maymon C. Exploration of Relations between Belief-Tracking and Motor Processing using a new Ecologically-Valid Helping Task for Adults. [Internet] [Doctoral dissertation]. Victoria University of Wellington; 2018. [cited 2019 Feb 22].
Available from: http://hdl.handle.net/10063/7800.

Council of Science Editors:

Maymon C. Exploration of Relations between Belief-Tracking and Motor Processing using a new Ecologically-Valid Helping Task for Adults. [Doctoral Dissertation]. Victoria University of Wellington; 2018. Available from: http://hdl.handle.net/10063/7800

24.
Rosso, Giovanni.
Généralisation du théorème de Greenberg-Stevens au cas du carré symétrique d'une forme modulaire et application au groupe de Selmer : Generalization of a theorem of Greenberg and Stevens to the case of the symmetric square of a modular form and an application to the Selmer group.

This thesis is devoted to the study of certain cases of a conjecture of Greenberg and Benois on derivative of p-adic L-functions using the method of Greenberg and Stevens. We first prove this conjecture in the case of the symmetric square of a parallel weight 2 Hilbert modular form over a totally real field where p is inert and whose associated automorphic representation is Steinberg in p, assuming certain hypotheses on the conductor. This is a direct generalization of (unpublished) results of Greenberg and Tilouine. Subsequently, we deal with the symmetric square of a finite slope, elliptic, modular form wich is Steinberg at p. To construct the two-variable p-adic L-function, necessary to apply the method of Greenberg and Stevens, we have to appeal to the recently developped theory of nearly overconvergent forms of Urban. We further strengthen the above result, removing the assumption that the conductor of the form is even, using the construction of the p-adic L-function by Böcherer and Schmidt. In the final chapter we recall the definition and the calculation of the algebraic ℒ-invariant à la Greenberg-Benois, and explain how some of the above-mentioned results could generalized to higher genus Siegel modular forms.

Rosso, Giovanni. “Généralisation du théorème de Greenberg-Stevens au cas du carré symétrique d'une forme modulaire et application au groupe de Selmer : Generalization of a theorem of Greenberg and Stevens to the case of the symmetric square of a modular form and an application to the Selmer group.” 2014. Web. 22 Feb 2019.

► Herein I investigate the nature and emergence of social representations of shale gas development (often called "fracking"). Social representations are common sense understandings of complex,…
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▼ Herein I investigate the nature and emergence of social representations of shale gas development (often called "fracking"). Social representations are common sense understandings of complex, novel phenomena generated in the public sphere via communal discourse. I triangulate between results from (1) a content analysis of regional newspaper coverage, (2) in-depth interviews, (3) field visits to communities discussing and engaged in development, and (4) a survey of residents in areas experiencing development and/or heightened discourse about potential development. My results reveal that these representations: (1) are limited in scope, (2) often relate to difficult to quantify social effects of development that are value-based, (3) are ethically-derived, (4) are historically-, culturally-, and socially-dependent, and (5) predict (rather than derive from) beliefs about effects of development. The grounding of key representations in values and ethical considerations intimates a very different public understanding of this issue than one in which representations are based primarily on potential economic and environmental effects of shale gas development, such as job creation and water contamination. The limited scope of representations highlights an expansive range of topics that are neglected in discourse on shale gas development. The causal primacy of summary views of development over beliefs about effects of development is this dissertation's most striking finding. Contrary to much empirical research on public perceptions of development and theoretical background applied to understanding these perceptions, both the data herein and social representations theory support valenced positions on shale gas development leading to beliefs about likelihood of impacts of development occurring, and to beliefs about the effects of those impacts on quality of life. This connotes substantial challenges for communicating about shale gas development in a way that affects summary views on this issue; likewise it portends further obstacles to alighting on policies/regulation of development that the public will broadly accept. I discuss the implications of all the aforementioned findings for communication about and policy on shale gas development. Finally, I reflect on the value of social representations theory for studying social psychology of energy development and offer recommendations for further improving the methodological rigor of social representations research.
Advisors/Committee Members: McComas, Katherine Anne (committeeMember), Stedman, Richard Clark (committeeMember), Brown, David L (committeeMember), Walter, Michael Todd (committeeMember), Decker, Daniel Joseph (committeeMember), McComas, Katherine Anne (committeeMember).

► According to some (e.g. Friston, 2010) predictive processing (PP) models of cognition have the potential to offer a grand unifying theory of cognition. The framework…
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▼ According to some (e.g. Friston, 2010) predictive processing (PP) models of cognition have the potential to offer a grand unifying theory of cognition. The framework defines a flexible architecture governed by one simple principle - minimise error. The process of Bayesian inference used to achieve this goal results in an ongoing flow of prediction that both makes sense of perception and unifies it with action. Such a provocative and appealing theory naturally has caused ripples in philosophical circles, prompting several commentaries (e.g. Hohwy, 2012; Clark, 2016). This thesis tackles one outstanding philosophical problem in relation to PP - the question of mental representation. In attempting to understand the nature of mental representations in PP systems I touch on several contentious points in philosophy of cognitive science, including the explanatory power of mechanisms vs. dynamics, the internalism vs. externalism debate, and the knotty problem of proper biological function. Exploring these issues enables me to offer a speculative solution to the question of mental representation in PP systems, with further implications for understanding mental representation in a broader context. The result is a conception of mind that is deeply continuous with life. With an explanation of how normativity emerges in certain classes of self-maintaining systems of which cognitive systems are a subset. We discover the possibility of a harmonious union between mechanics and dynamics necessary for making sense of PP systems, each playing an indispensable role in our understanding of their internal representations.

► The wavelet transform is a well studied and understood analysis technique used in signal processing. In wavelet analysis, signals are represented by a sum of…
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▼ The wavelet transform is a well studied and understood analysis technique used in signal processing. In wavelet analysis, signals are represented by a sum of self-similar wavelet and scaling functions. Typically, the wavelet transform makes use of a fixed set of wavelet functions that are analytically derived. We propose a method for learning wavelet functions directly from data. We impose an orthogonality constraint on the functions so that the learned wavelets can be used to perform both analysis and synthesis. We accomplish this by using gradient descent and leveraging existing automatic differentiation frameworks. Our learned wavelets are able to capture the structure of the data by exploiting sparsity. We show that the learned wavelets have similar structure to traditional wavelets.
Machine learning has proven to be a powerful tool in signal processing and computer vision. Recently, neural networks have become a popular and successful method used to solve a variety of tasks. However, much of the success is not well understood, and the neural network models are often treated as black boxes. This thesis provides insight into the structure of neural networks. In particular, we consider the connection between convolutional neural networks and multiresolution analysis. We show that the wavelet transform shares similarities to current convolutional neural network architectures. We hope that viewing neural networks through the lens of multiresolution analysis may provide some useful insights.
We begin the thesis by motivating our method for one-dimensional signals. We then show that we can easily extend the framework to multidimensional signals. Our learning method is evaluated on a variety of supervised and unsupervised tasks, such as image compression and audio classification. The tasks are chosen to compare the usefulness of the learned wavelets to traditional wavelets, as well as provide a comparison to existing neural network architectures. The wavelet transform used in this thesis has some drawbacks and limitations, caused in part by the fact that we make use of separable real filters. We address these shortcomings by exploring an extension of the wavelet transform known as the dual-tree complex wavelet transform. Our wavelet learning model is extended into the dual-tree domain with few modifications, overcoming the limitations of our standard model. With this new model we are able to show that localized, oriented filters arise from natural images.

► Cognitive psychologists have developed many formal models of categorization, but they have been almost exclusively tested using artificial categories because deriving psychological representations of natural…
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▼ Cognitive psychologists have developed many formal models of categorization, but they have been almost exclusively tested using artificial categories because deriving psychological representations of natural stimuli using traditional methods such as multidimensional scaling (MDS) has been an intractable task. In this dissertation, I show that deep convolutional neural networks (CNNs) may be used to solve this problem. First, I provide an overview of how CNNs work, and I review related work that has examined the relationship between the representations learned by CNNs and the psychological representations used by humans. I then demonstrate that CNNs can be trained to predict the MDS coordinates of rocks derived in previous work (Nosofsky, Sanders, Meagher, & Douglas, 2017). In Experiment 1, I conduct a conceptual replication of Nosofsky et al.’s (2017) methods and demonstrate that similar MDS dimensions emerge across different sets of rocks, and the CNNs are able to generalize from one set to the other. Then in Experiment 2, I conduct a categorization experiment and demonstrate that the CNN representations can be used in conjunction with a formal cognitive model to predict human behavior, indicating that CNNs can be used to automate MDS studies in the future.
Advisors/Committee Members: Nosofsky, Robert (advisor).

► Langlands' functoriality conjectures predict how automorphic representations of different groups are related to one another. Automorphic induction is a basic case of functoriality motivated by…
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▼ Langlands' functoriality conjectures predict how
automorphic representations of different groups are related to one
another. Automorphic induction is a basic case of functoriality
motivated by Galois theory. Let F be a local field of
characteristic 0. The local Langlands correspondence for GL(N)
states that there is a bijection between N-dimensional, complex
representations of the Weil-Deligne group W_F' and irreducible,
admissible representations of GL(N,F). Given an operation on Weil
group representations, one can ask what the corresponding operation
is for representations of GL(N,F). Automorphic induction is the
operation on representations of GL(N,F) corresponding to induction
of representations of the Weil group. Given a cyclic extension E of
F of degree D, automorphic induction is a mapping of
representations of GL(M,E) to representations of GL(MD,F). Once
automorphic induction has been established for local fields, one
can ask if the operation applied at each local component of an
automorphic representation produces another automorphic
representation. The automorphic induction problem was first
considered in detail by Kazhdan. Kazhdan proved the local
automorphic induction map exists in the of M=1. The next major
result is due to Arthur-Clozel, where it was shown that a global
automorphic induction operation exists for prime degree extensions.
The local theory was completed by Henniart and Herb; they showed
that the local automorphic induction map exists for arbitrary M and
cyclic extensions of arbitrary degree. Moreover, Henniart showed
later that the local automorphic induction map is consistent with
induction of Weil group representations and the local Langlands
correspondence. Finally, Henniart extended the results of
Arthur-Clozel to cyclic extensions of any degree and verified that
the resulting mapping of automorphic representations is consistent
with the local lifting. All of these results rely on some version
of the trace formula and powerful theorems about L-functions for
GL(N). The goal of this thesis is to give a different proof of
local and global automorphic induction when M=1 and to emphasize
some different aspects of the theory. As with the results
previously mentioned, the main technical tool is a trace formula,
specifically the full global trace formula of Arthur. The proof
relies more on the trace formula and less on L-functions than
previous proofs. Chapter 1 consists of background and preliminaries
needed to state the main theorems on local and global automorphic
induction. We also discuss various results that are needed to state
Arthur's trace formula. In Chapter 2, we give a statement of the
relevant trace formulas. We also discuss some computations in
general rank that could be used in a generalization of our
techniques to the case of M>1. The main local and global
theorems are established in Chapter 3. As with most trace formula
arguments, the proof boils down to an application of linear
independence of characters.
Advisors/Committee Members: Cogdell, James (Advisor).

The aim of this thesis is to investigate the topic of edge-colourings of graphs in the context of hereditary graph properties. We particularly aim…
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▼

M.Sc.

The aim of this thesis is to investigate the topic of edge-colourings of graphs in the context of hereditary graph properties. We particularly aim to investigate analogues of reducibility, unique factorization and some related concepts. Chapter 1 gives the basic definitions and terminology. A few useful general results are also stated. In Chapter 2 we define and investigate decomposability, the analogue of reducibility. Some general results are first proved, such as that the indecomposability of an additive induced-hereditary property in the lattice of such properties implies that it is indecomposable in a general sense. The decomposability of various specific properties is then investigated in the rest of the chapter. In Chapter 3 we investigate unique decomposability, the analogue of unique factorization. We give examples showing that not every additive hereditary property is uniquely decomposable, and we obtain some results on homomorphism properties which lead to the unique decomposability of Ok. We also consider some related questions, such as cancellation and preservation of strict inclusions. Chapter 4 deals with Ramsey properties. We obtain some general results and, using the so-called partite construction, we obtain a few restricted Ramsey-graph results. As a corollary, we obtain two more unique decomposability results. In Chapter 5 we obtain various bounds involving the property Vk of k-degeneracy. We also investigate the sharpness of these bounds and prove that Vk is indecomposable for every k. Chapter 6 deals with the connection between colourings of infinite graphs and properties of finite graphs. We obtain some extensions of the Compactness Principle and give an example showing that the Compactness Principle can be useful in studying finite graphs.